Stress field parameter

Secondly, Irwin 6) found that the stress field around a sharp crack in a linear elastic material could be uniquely defined by a parameter named the stress-intensity factor, K and stated that fracture occurs when the value of K, exceeds some critical value, K C. Thus, K, is a stress field parameter independent of the material whereas Klc, often referred to as the fracture toughness, is a measure of a material property. Again the subscript I is used to denote the tensile-opening mode. 

The second approach, due to lrwin is to characterise the stress field surrounding a crack in a stressed body by a stress-field parameter K (the stress intensity factor ). Fracture is then supposed to occur when K achieves a critical value K - Although, like Griffith s equation, this formulation of fracture mechanics is based on the assumptions of linear elasticity, it is found to work quite effectively provided that inelastic deformations are limited to a small zone around the crack tip. Like, however, the critical parameter remains an empirical quantity it cannot be predicted or related explicitly to the hysical properties of the solid. Like,, K. is time and temperature de ndent. 

Wambach et al (1968) use the term fracture toughness for the parameter sometimes referred to as the fracture energy many authors refer to Irwin s critical stress field parameter (see... 

Second, Irwin found that the stress field surrounding a crack could be defined uniquely by a stress-field parameter termed the stress-intensity factor, K. He postulated that fracture occurs when the value of K exceeds some critical value. K, often referred to as the material fracture toughness. Thus K relates the magnitude of the stress-intensity local to the crack in terms of the applied loadings and the geometry of the structure in which the crack is located. A crack in a solid may be stressed in three different modes as depicted in Fig. 2.18. Mode I opening, and hence the Mode I value for the stress intensity factor Ki, is the most critical situation in bonded joints. 

Different formulations of fracture mechanics provide different fracture parameters. Linear elastic fracture mechanics (LEFM)(D defines a stress field parameter K which reflects the overall intensity of the stress field around the crack. Failure occurs when K achieves its critical value K. The formula for K depends on the test specimen configuration, but for a central crack of half-length c in a semi-infinite sheet, for example, it is given by... 

Stress field parameter Critical stress field parameter Peeling length Peeling rate... 

NUMERICAL ANALYSIS OF THE STRESS FIELD PARAMETERS IN THE FRACTURE PROCESS ZONES IN CONCRETE... 

Restoring of SD of parameters of stress field is based on the effect of acoustoelasticity. Its fundamental problem is determination of relationship between US wave parameters and components of stresses. To use in practice acoustoelasticity for SDS diagnosing, it is designed matrix theory [Bobrenco, 1991]. For the description of the elastic waves spreading in the medium it uses matrices of velocity v of US waves spreading, absolute A and relative... 

Relationship of temporary parameters of US signals with parameters of stresses field under... 

The use of the single parameter, K, to define the stress field at the crack tip is justified for brittle materials, but its extension to ductile materials is based on the assumption that although some plasticity may occur at the tip the surrounding linear elastic stress field is the controlling parameter. 

The utility of K or any elastic plastic fracture mechanics (EPFM) parameter to describe the mechanical driving force for crack growth is based on the ability of that parameter to characterize the stress-strain conditions at the crack tip in a maimer which accounts for a variety of crack lengths, component geometries and loading conditions. Equal values of K should correspond to equal crack tip stress-strain conditions and, consequently, to equivalent crack growth behavior. In such a case we have mechanical similitude. Mechanical similitude implies equivalent crack tip inelastic zones and equivalent elastic stress fields. Fracture mechanics is... 

In a recent attempt to bring an engineering approach to multiaxial failure in solid propellants, Siron and Duerr (92) tested two composite double-base formulations under nine distinct states of stress. The tests included triaxial poker chip, biaxial strip, uniaxial extension, shear, diametral compression, uniaxial compression, and pressurized uniaxial extension at several temperatures and strain rates. The data were reduced in terms of an empirically defined constraint parameter which ranged from —1.0 (hydrostatic compression) to +1.0 (hydrostatic tension). The parameter () is defined in terms of principal stresses and indicates the tensile or compressive nature of the stress field at any point in a structure —i.e.,... 

In many cases of transport in solids, the atoms (ions) of one sublattice of the crystal are (almost) immobile. Here, we can identify the crystal lattice with the external (laboratory) frame and define the fluxes relative, to this immobile sublattice (to = 0). v° is bk-Xk (Eqn. (4.51)) where Xk is the sum of all local forces which can be applied externally (eg., an electric field), or which may stem from fields induced by the, (Fickian) diffusion process itself (eg., self-stresses). An example of such a diffusion process that leads to internal forces is the chemical interdiffusion of A-B. If the lattice parameter of the solid solution changes noticeably with concentration, an elastic stress field builds up and acts upon the diffusing particles, it depends not only on the concentration distribution, but on the geometry of the bounding crystal surfaces as well. 

Most force fields used in coordination chemistry, in respect of the organic part of the molecules, are based on or are at least similar to the MM2 11 or AMBER 11 parameterization schemes, or mixtures thereof. However, it is of importance to stress again that transferring parameters from one force field to another without appropriate checks is not valid. This is not only a question of the different potential energy functions that may be used, but it is also a consequence of the interrelatedness of the entire set of parameters. Force field parameters imported from any source, whether a well-established force field or experimental data, should only be used as a starting point for further parameter refinement. 

The parameter K is the stress intensity factor, whose level defines the stress field around the crack tip. In the case of a mode I loading, it is denoted as Kj. 

When the experimentalist set an ambitious objective to evaluate micromechanical properties quantitatively, he will predictably encounter a few fundamental problems. At first, the continuum description which is usually used in contact mechanics might be not applicable for contact areas as small as 1 -10 nm [116,117]. Secondly, since most of the polymers demonstrate a combination of elastic and viscous behaviour, an appropriate model is required to derive the contact area and the stress field upon indentation a viscoelastic and adhesive sample [116,120]. In this case, the duration of the contact and the scanning rate are not unimportant parameters. Moreover, bending of the cantilever results in a complicated motion of the tip including compression, shear and friction effects [131,132]. Third, plastic or inelastic deformation has to be taken into account in data interpretation. Concerning experimental conditions, the most important is to perform a set of calibrations procedures which includes the (x,y,z) calibration of the piezoelectric transducers, the determination of the spring constants of the cantilever, and the evaluation of the tip shape. The experimentalist has to eliminate surface contamination s and be certain about the chemical composition of the tip and the sample. 

The volumetric constitutive equations for a chemoporoelastic material can be formulated in terms of the stress S = a,p, it and the strain 8 = e, (, 9, i.e., in terms of the mean Cauchy stress a, pore pressure p, osmotic pressure it, volumetric strain e, variation of fluid content (, and relative increment of salt content 9. Note that the stress and strain are measured from a reference initial state where all the stress fields are equilibrated. The osmotic pressure it is related to the change in the solute molar fraction x according to 7r = N Ax where N = RT/v is a parameter with dimension of a stress, which is typically of 0( 102) MPa (with R = 8.31 J/K mol denoting the gas constant, T the absolute temperature, and v the molar volume of the fluid). The solute molar fraction x is defined as ms/m with m = ms + mw and ms (mw) denoting the moles of solute (solvent) per unit volume of the porous solid. The quantities ( and 9 are defined in terms of the increment Ams and Amw according to... 

The measurement of residual stresses is usually associated with the analysis of mechanical properties, and not microstructure. However, residual stress fields in nanocomposites depend directly on microstructural parameters (particle size, position and spacing), as well as bulk material properties, such as differences in the coefficient of thermal expansion. 

In the solid state deformation, the nonlinear viscoelastic effect is most clearly shown in the yield behavior. The activation volume tensor is a key parameter. In addition to the well known dependence of yield stress on temperature and strain rate, the functional relationships between yield, stress field, and physical aging are presented. 

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